Mathematics Question involving Conics (Hyperbola & Ellipse)

• DevilMgi

  16 Apr 11, 18:02

  http://a4.sphotos.ak.fbcdn.net/hphotos-ak-snc6/216117_10150165072049081_650844080_6749510_2002095_n.jpg Hi all! I Sincerely appreciate any help that can be given for this question.. I'm at a lost. Thank you so much in advance!! :)
• wee_ws

  16 Apr 11, 18:24

  Hi,

    Try and draw a diagram to better visualise the problem. Thanks.

  Cheers,
  Wen Shih

• DevilMgi

  16 Apr 11, 18:35

  Hi Wen Shih! thank you for your input. But I'm really lost.. Don't have the slightest clue on how to start the question.. I spend an hour drawing the diagram, but I think I'm missing out on some formula that wasn't in my notes. All i have are the general formula for hyperbola and ellipses. :( I'm particularly puzzled on how to solve for focal points, distance between focal point and point on graph, as well as understanding how PA being parallel to PF can help me to solve the question. Any idea? :P
• DevilMgi

  16 Apr 11, 21:14

  ok, i think i solved part 1. Ellipse C = ((x^2)/36) + ((y^2)/20) = 1 anyone with any idea for part 2 and 3 of the qn?
• wee_ws

  18 Apr 11, 20:20

  Hi,

    Your answer for (1) is correct.

    The centre of the hyperbola is at the origin. The hyperbola has vertices at (-4, 0) and (4, 0). Each focus of the hyperbola is c units from the centre, where

    c^2 = 16 + 20 (the sum of the denominators),

    from which we obtain c = 6.

    Now, the equation of the ellipse is

    (x^2 / 6^2) + (y^2 / b^2) = 1, where b is to be found.

    The centre of the ellipse is at the origin. Each focus is 4 units from the centre, where

    4^2 = 6^2 - b^2 (the difference of the denominators),

    from which we obtain b^2 = 20.

    For (2):

    1. Let position vector of P be xi + yj.

    2. Form the vectors PA and PF.

    3. Form an equation, given the zero scalar product of vectors PA and PF.

    4. With the equation obtained for the ellipse, solve the equation in step 3.

    Is this a question from IB Maths HL?

    Thanks.

  Cheers,
  Wen Shih

• wee_ws

  18 Apr 11, 20:27

  Hi,

    The phrasing in (3) is odd and does not make sense. Thanks.

  Cheers,
  Wen Shih